## Kepler's Laws of Planetary Motion

"The diversity of the phenomena of nature is so great, and the treasures hidden in the heavens so rich, precisely in order that the human mind shall never be lacking in fresh nourishment.”

*Johannes Kepler*## College Board Objectives for this Unit

**Orbits of planets and satellites**

Students should understand the motion of an object in orbit under the influence of gravitational forces, so they can:

a) For a circular orbit:

(1) Recognize that the motion does not depend on the object’s mass; describe qualitatively how the

velocity, period of revolution, and centripetal acceleration depend upon the radius of the orbit; and

derive expressions for the velocity and period of revolution in such an orbit.

(2) Derive Kepler’s Third Law for the case of circular orbits.” (College Board, 2005)

Kepler’s Laws are organized into three main thoughts: 1) Law of Ellipses; 2) Law of Equal Areas; and 3) Harmonic Law. These explorations apply dimensions of complexity by focusing on inter-disciplinary connections with culture, religion and mathematics (Kaplan, 2005). You will go beyond rote application of Kepler’s Laws and apply methods of inquiry, investigation and research to discover these laws through observation and analysis.You may choose to explore these laws by (1) conducting research to obtain background information on Kepler and the religious and scientific beliefs of his era and gaining an understanding of the impact of Kepler’s proposal, (2) constructing models (physical or graphical) that represent planetary motion in accordance with Kepler’s findings, or finally, (3) exploring the laws quantitatively through an experiment that requires data analysis, the development of mathematical models, and drawing conclusions from those models. Students choosing option 1 are The Researchers, option 2, The Modelers, and option 3 students are The Analyzers. |
The Researchers review web-based and hard-copy references to gain an understanding of the scientific and religious communities’ reactions to the publishing of Kepler’s Laws. This group gains an understanding of the relationship between religion, culture, and science and discusses the impact of these factors on Kepler’s work and on successive work. The group continues their research to discover the impact of Kepler’s work on future scientific discoveries, specifically Newton’s Law of Universal Gravitation and Einstein’s Theory of Relativity, and presents their findings through a bulletin board, video, or Microsoft PowerPoint or Photo Story.The Modelers use a telescope equipped with a measuring scale to collect moon diameter data. Since the moon’s diameter appears larger when the moon is closer to the earth and smaller when the moon is farther from the earth, the students can utilize this data to construct the path of the moon’s orbit. use CLEA (Contemporary Laboratory Experiences in Astronomy) software that simulates an observatory to obtain orbital information about Jupiter’s moons (Gettysburg College, 1997). This software allows students to take on the role of astronomer and view virtual images of planetary satellites. The students use the software to determine the mass of Jupiter.The Analyzers |

**References:**

College Board. (2005).

*Learning Objectives for AP Physics.*Retrieved June 13, 2008, from AP Central:

http://apcentral.collegeboard.com/apc/members/repository/ ap05_phys_objectives_45859.pdf.

Gettysburg College Department of Physics. (1997, October 6).

*The Revolution of the Moons of Jupiter*. Retrieved

April 5, 2009, from Project CLEA: http://www3.gettysburg.edu/~marschal/clea/CLEAhome.html

Kaplan, S. N. (2005). Layering Differentiated Curricula for the Gifted and Talented. In F. A. Karnes, & S. M. Bean,

*Methods and Materials for Teaching the Gifted*(pp. 107-131). Waco, TX: Prufrock Press, Inc.